Analysis of Chirp as windowing function through fractional Fourier transform

Abstract

This article presents a new mathematical model for obtaining the fractional Fourier transform (FrFT) of Chirp function. FrFT is a parameterised transform having an adjustable transform parameter which makes it more flexible and superior over ordinary FT in several applications. It is an important tool used in signal processing for spectral analysis. The closed-form expression derived for FrFT of finite duration Chirp establishes the dependence of FrFT of Chirp on the order of FrFT and the Chirp parameter. The mathematical model obtained shows that the Chirp function can be used as an adjustable window function in the fractional Fourier domain. The main-lobe width, side-lobe level and side-lobe fall-off rate of a Chirp window can be controlled by changing the adjustable transform parameter to different values. For some particular values of fractional angle, Chirp can give better spectral parameters than the existing window functions. By varying the order of FrFT, the variations in spectral parameters of the Chirp window are obtained and studied. The performance of the Chirp window in fractional domain is also compared with some of the existing windows.